Markov random fields are a popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for provably learning them relied on exhaustive search, correlation decay or various incoherence assumptions. Bresler gave an algorithm for learning general Ising models on bounded degree graphs. His approach was based on a structural result about mutual information in Ising models. Here we take a more conceptual approach to proving lower bounds on the mutual information.

Sampling in discrete spaces, with critical applications in simulation and optimization, has recently been boosted by significant advances in gradient-based approaches that exploit modern accelerators like GPUs. However, two key challenges are hindering further advancement in research on discrete sampling.

From a Bayesian perspective, they offer a realistic modeling of data priors and facilitate solving inverse problems through posterior sampling.

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Asynchronous Gibbs sampling has been recently shown to be fast-mixing and an accurate method for estimating probabilities of events on a small number of variables of a graphical model satisfying Dobrushin's condition [DSOR16].

Structure learning is the task of finding the dependency graph of a Markov random field (MRF) given i.i.d.

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